People will lose money from bitcoin because LN was hacked in some way, and they won't blame LN... it'll just fall on bitcoin.
No. Just like the fact that people lose money when their computer gets hacked doesn't weaken Bitcoin. "Be your own bank" comes with responsibilities, or to state the obvious: "it's a feature, not a bug".
But if LN's ledger system is as infallible as bitcoin's, then I guess there's nothing to worry about.
There is no ledger system, it's just two people with their own LN wallet. There could be a few hubs involved, but the only way to lose your money is if you lose your wallet.